Machine Learning in Indoor Positioning and Channel Prediction Systems. Yizhou Zhu B.Eng., Zhejiang University, 2010

Transcription

1 Machine Learning in Indoor Positioning and Channel Prediction Systems by Yizhou Zhu B.Eng., Zhejiang University, 2010 A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF APPLIED SCIENCE in the Department of Electrical and Computer Engineering c Yizhou Zhu, 2018 University of Victoria All rights reserved. This thesis may not be reproduced in whole or in part, by photocopying or other means, without the permission of the author.

2 ii Machine Learning in Indoor Positioning and Channel Prediction Systems by Yizhou Zhu B.Eng., Zhejiang University, 2010 Supervisory Committee Dr. Xiaodai Dong, Supervisor (Department of Electrical and Computer Engineering) Dr. Wu-Sheng Lu, Departmental Member (Department of Electrical and Computer Engineering)

3 iii Supervisory Committee Dr. Xiaodai Dong, Supervisor (Department of Electrical and Computer Engineering) Dr. Wu-Sheng Lu, Departmental Member (Department of Electrical and Computer Engineering) ABSTRACT In this thesis, the neural network, a powerful tool which has demonstrated its ability in many fields, is studied for the indoor localization system and channel prediction system. This thesis first proposes a received signal strength indicator (RSSI) fingerprinting-based indoor positioning system for the widely deployed WiFi environment, using deep neural networks (DNN). To reduce the computing time as well as improve the estimation accuracy, a two-step scheme is designed, employing a classification network for clustering and several regression networks for final location prediction. A new fingerprinting, which utilizes the similarity in RSSI readings of the nearby reference points (RPs) is also proposed. Real-time tests demonstrate that the proposed algorithm achieves an average distance error of 43.5 inches. Then this thesis extends the ability of the neural network to the physical layer communications by introducing a recurrent neural network (RNN) based approach for real-time channel prediction which uses the recent history channel state information (CSI) estimation for online training before prediction, to adapt to the continuously changing channel to gain a more accurate CSI prediction compared to the other conventional methods. Furthermore, the proposed method needs no additional knowledge, neither the internal properties of the channel itself nor the external features that affect the channel propagation. The proposed approach outperforms the other methods in a changing environment in the simulation test, validating it a promising method for channel prediction in wireless communications.

4 iv Contents Supervisory Committee Abstract Table of Contents List of Tables List of Figures Acknowledgements Dedication ii iii iv vii viii xii xiii 1 Introduction Overview Neural Network Indoor Localization with Deep Neural Network Channel State Information Prediction with Recurrent Neural Network Summary of Contributions Organizations Neural Network Perceptron An Example of Perceptron Implementing Logic AND Linear Unit and Gradient Descent Linear Unit Objective Function Gradient Descent

5 v 2.3 Neural Network and Backpropagation Neuron Neural Network Backpropagation Recurrent Neural Network and Backpropagation Through Time Recurrent Neural Network Backpropagation Through Time Gradient Vanishing and Explosion Long Short Term Memory Networks Forward for Value Backward for Error Gradient Deep Neural Network in Indoor Positioning System with a Two- Step Scheme Introduction Related Work Fingerprinting Technique NN based IPSs Clustering based IPSs System Model Database building Clustering Localization Filtering Experiment And Analysis Experimental Setup Clustering Test Final Localization Test Conclusions Recurrent Neural Network in Channel Prediction with an Online Training Scheme Introduction Related Work

6 vi Conventional Techniques Neural Network based Techniques System Model Problem Formulation Recurrent Neural Network Network Structure Model Training and Testing Timing Schedule Experiment And Analysis Experimental Setup Impact of the Normalized Doppler Shift Impact of the Base Station Angular Parameters Impact of the SNR Impact of the Normalized Doppler Shift and the SNR Impact of the Number of RNN Units K and the Known History Length P Conclusions Conclusions DNN based RSSI fingerprinting Indoor localization Real-time CSI Prediction Approach using RNN Future Work A Key Python Code for Indoor Localization with a Two-Step Scheme 62 B Key Python Code for Channel Prediction with an Online Training Scheme 65 Bibliography 70

7 vii List of Tables Table 2.1 Truth Table of the Logic AND Table 3.1 Parameter used for training in Classification and Localization networks Table 3.2 Mean localization error and Standard deviation of different methods 37 Table 4.1 Parameters used for SCM Table 4.2 Parameters used for network configuration and training

8 viii List of Figures Figure 2.1 A Simple Perceptron Figure 2.2 A Simple Linear Unit Figure 2.3 A Simple Fully Connected Neural Network Figure 2.4 A Simple Recurrent Neural Network Figure 2.5 The Structure of a LSTM Cell Figure 3.1 The three-wheel robot developed by my colleagues Figure 3.2 (a) Floor map of surveillance area which could be divided into 5 clusters. (b) Heat map of the RSSI strength from 6 APs used in our localization scheme Figure 3.3 CDF of localization errors Figure 4.1 SCM channle, and the Prediction Setup Figure 4.2 Structure of one RNN Unit Figure 4.3 Network Structure Figure 4.4 Process of Predicting N Unknowns Figure 4.5 Timing Schedule Figure 4.6 Sample Prediction and Ground Truth Figure 4.7 Performance Comparison - Normalized Doppler Shift changes from to 0.01 evenly and SNR = 20 db Figure 4.8 Performance Comparison - Normalized Doppler Shift changes from to 0.01 evenly and SNR = 15 db Figure 4.9 Performance Comparison - Normalized Doppler Shift changes from to 0.01 evenly and SNR = 10 db Figure 4.10Performance Comparison - Base Station Angular Parameters (ThetaBs) changes from 180 to 180 evenly Figure 4.11Performance Comparison - SNR changes from 20 db to 10 db evenly

9 ix Figure 4.12Performance Comparison - Normalized Doppler Shift changes from 0.01 to and SNR changes from 20 db to 10 db evenly 57 Figure 4.13Performance Comparison - Different Value of K Figure 4.14Performance Comparison - Different Value of P

10 x List of Abbreviations AR Autoregressive BEM Basis-Expansion Model CDF Cumulative Distribution Function CE Complex Exponential CNN Convolutional Neural Network CSI Channel State Information DANN Discriminant-Adaptive Neural Network DNN Deep Neural Network DPS Discrete Prolate Spheroidal ELM Extreme Learning Machine FDD Frequency Division Duplex GNSS Global Navigation Satellite Systems GPS Global Positioning System GRNN Generalized Regression Neural Network IPS Indoor Positioning System KNN K Nearest Neighbours LBS Location-based Service LMS Least Mean Squares LSTM Long Short Term with Memory MDA Multiple Discriminant Analysis ME Minimum-Energy MIMO Multiple Input Multiple Output

11 xi ML Maximum Likelihood MLP Multilayer Perceptron MMSE Minimum Mean Square Error mmwave Millimetre Wave MSE Mean Square Error NN Neural Network PCA Principal Component Analysis PRC Parametric Radio Channel RFID Radio Frequency Identification RLS Recursive Least Squares RNN Recurrent Neural Network RP Reference Point RSSI Received Signal Strength Indicator SCM Spatial Channel Model SISO Single Input Single Output SVM Support Vector Machine TDD Time Division Duplex WLAN Wireless Local Area Network

12 xii ACKNOWLEDGEMENTS I would like to thank: My wife, my family and my cat seven for supporting me in the low moments. It was the hardest two years for us, but also the most unforgettable, during which we got married and adapted to the new life here in Victoria. I would like to express my endless gratitude to my wife, Yue, for her love, support and encouragement. Supervisor Dr. Xiaodai Dong for mentoring, support, encouragement, and patience. It was so simple a phone call three years ago which made it real that I could be here to study and research. Furthermore, her guidance, support and encouragement paved the way for me as a researcher, to open mind and think different. Dr. Tao Lu and Dr. Wu-Sheng Lu for mentoring and guidance. They have provided me with professional guidance and suggestions about the projects that I involved in and the way of thinking. My colleagues and my friends for their support and help in the last two years. It is them that made the journey here full of memory and pleasure. I would thank my colleagues, Minh Tu Hoang, Ahmed Magdy Elmoogy, Tyler Reese, Brosnan Yuen, Yiming Huo, Jun Zhou, Ping Cheng, and my friends, Weizheng Li, Ji Shi, Kris Haynes, Jeff Martens for all the thing you guys have done for me and my family. Yizhou Zhu Victoria, BC, Canada July, 2018

13 xiii DEDICATION To my wife, my family for Everytyhing you have done.

14 Chapter 1 Introduction 1.1 Overview Though much of the theory was developed 20 years ago, neural networks (NNs) have become very popular in recent years because of the expanding data and the development of the computing infrastructure. With recent events such as the Go match between the 18-time world champion Lee Sedol and AlphaGo, a Go program developed by Deepmind, machine learning has received more and more attention. As a result of Moore s Law, the computing power doubles every 18 months over the past decades. Although GPUs are designed for output to a display device, its parallel computing power is well-suited for training NNs, which are structured in a very uniform manner such that at each layer of the network identical artificial neurons perform the same computation. In this thesis, we proposed two neural network applications for indoor localization and physical layer communication respectively, to explore the ability of neural networks in different areas Neural Network A neural network system is a system that processes data in a way that biological neurons do. Unlike the other expert systems that need task-specific programming, it can learn logic or relation inside of the large data instead of a given model. An NN is based on several collections of nodes called neurons which are connected with each other in a particular way. A neuron that takes the input from other neurons can process it and then send the result to the connected neurons for further use. The

15 2 network processes the input this way and compares the output of the network itself with the corresponding known result. Then adjustment based on the error is fed back into the network to modify the weights of the neurons inside to learn from the data. There are three dominant type of NNs that are widely used now, deep neural network (DNN), convolutional neural network (CNN) and recurrent neural network (RNN), which are defined by the network architecture. DNN is a network that has multiple hidden layers between the input and output layer to enable the ability to model complex non-linear system. DNNs are typically feedforward networks in which data flows from the input layer to the output layer without looping back. Multilayer perceptron (MLP) is a commonly used feedforward DNN and uses backpropagation to train, which has at least three layers of neurons, and each layer uses a nonlinear activation function except the input layer. CNN uses a variation of MLP, which has been successfully applied in visual recognition and classification. A CNN usually consists of convolutional layers, pooling layers, fully connected layers and normalization layers. A CNN is easier to train and have many fewer parameters than fully connected networks with the same number of hidden units. RNN is a type of NN that the neurons do not always feedforward, but connect to the neurons in the previous layer or the current layer itself. Thus RNN can use their internal state or memory to process the input so it is suitable for problems that can be formulated into a time sequence Indoor Localization with Deep Neural Network As the fast development of the wireless communication and mobile devices, the location-based services (LBSs) have been driven so fast in many application scenes, which raises a massive demand for high accuracy of localization. Although global navigation satellite systems (GNSS) is widely used in the outdoor environment to obtain

16 3 a highly accurate location estimate, it is still a challenge in indoor areas as the GNSS signals from satellites cannot often be seen. Thus an accurate indoor positioning system (IPS) became a fundamental problem for many upper-level applications. A WiFi based IPS is a promising approach for human because of the widely deployed WiFi infrastructure and the fast increasing WiFi-enabled mobile devices, which makes the system low cost and easy to deploy. Although different sensor-based systems are widely studied, such as Bluetooth [1, 35], radio frequency identification (RFID) [20] and ultrasound [33], they often focus on objective tracking and need corresponding hardware. IPS could be classified into two classes, ranging based and fingerprinting based. Ranging based ones derive distance between the transmitter and receiver by using different kinds of sensor data and assuming a particular propagation model [22] and then calculate the position based on triangulation. However, due to the changing environment and the multi-path phenomenon, its performance is not comparable to the fingerprinting approaches, which associates a group of physical measurements at each reference point (RP) as a fingerprint, perform like pattern matching systems, comparing the similarity between the target fingerprint and those in the database to return the best match to be the estimation. Some conventional experts system used in IPSs includes K nearest neighbours (KNN) [4, 29, 39, 42], support vector machine (SVM) [34, 21], filter-based [5, 3] and NN based [14, 19, 7, 24] algorithms. Depending on the output type of the network, existing NN based IPSs can be grouped into two categories, classification and regression. The classification type outputs the predicted label of the unknown location while the regression type directly returns the exact coordinates. In the literature, DNN [14, 19] is the most frequently used NN for IPS while CNN [7] and RNN [24] are also implemented in some ways Channel State Information Prediction with Recurrent Neural Network Since the rapid development of machine learning in a wide range of applications, researchers explore its employment in communication, such as radio resource management, network optimization and other higher layer aspects. Physical layer designs are also studied, ranging from channel estimation and detection [40], decoding [28, 16] to equalization [8, 10], spectrum usage recognition [15], etc.

17 4 Classical communication theory develops statistic models based on assumptions. But 5G and future generation systems may employ a large number of antennas when millimetre wave (mmwave) bands are used, accurate modelling using classical theory is increasingly difficult and complex. Thus machine learning based systems become a promising solution as they establish the internal relationship, which is not easily describable by mathematical formulas, based on a large number of training data. Obtaining channel state information (CSI) is vital to both transmitter and receiver for high spectral efficiency. Due to the instability of the wireless propagation channel caused by user mobilities and changing dynamics in the environment, a pilot based technique is applied by transmitting known pilot symbols, also called reference symbols, between transmitter and receiver to estimate the channel in real time and then interpolate or extrapolate CSI estimation at non-pilot positions. Channel estimation is often done on the receiver side, thus for the transmitter to know the channel, either CSI feedback is required in frequency division duplex (FDD) or pilots are transmitted in the opposite direction and assume channel reciprocity in time division duplex (TDD). The resource consumed and the time delay caused by the feedback is significant for CSI estimation in a fast-changing channel. Therefore, channel prediction is very useful in this case [13, 12]. The conventional channel prediction techniques can be divided into three groups, the parametric radio channel (PRC) model [2, 36], basis-expansion model (BEM) [41] and the autoregressive (AR) model [23, 17, 13, 18]. These methods predict CSI based on certain theoretical channel propagation models and/or estimation of channel long-term statistics and channel parameters. On the other hand, instead of deriving equations based on assumptions and propagation models, machine learning based approaches train a learning model, e.g., a DNN [11] or a CNN [25], using a large known dataset to find the internal relation underneath. The performance in simulation and/or extensive experiments shows these approaches are comparable to, or even better than the conventional methods. 1.2 Summary of Contributions In this thesis, the main results are presented in Chapters 3 and 4, which are summarized below. Chapter 3 presents a DNN based RSSI fingerprinting indoor localization system that reaches a result of 43.5 inches mean localization error with 84 % of its predictions

18 5 under the error of 60 inches as well as reduces the time complexity significantly compared to KNN models in real experiment test. The problem formulation, model establishment, database buildup are present and illustrated and a real experiment is performed to demonstrate the ability of NN in analyzing the RSSI readings and predicting location estimation for indoor localization. Based on the principal idea of fingerprinting systems, a new fingerprinting for RSSI based system is proposed by utilizing the similarity in RSSI readings between two closeby points. To reduce the computing time as well as improve the estimation accuracy, a scheme employing a classification network for clustering and several localization networks for final location prediction is designed. Furthermore, a median filter pre-processor is applied before the data is fed into the network, to reduce the impact of the RSSI fluctuation. Finally, real experiments performed in the lab area provides supportive results for our performance analysis. Chapter 4 investigates an online training based RNN real-time CSI prediction approach that has the best performance compared to the conventional AR model and the offline trained RNN. Since channel prediction is one of the fundamental techniques in wireless communication, the improvement in prediction achieved by the proposed system could further increase the channel bandwidth and enhance the stability. By introducing an online training scheme using the recent history data and a properly designed time schedule, the proposed system can then adapt to the continuously changing channel to give a better prediction with no additional knowledge of the channel. Initial simulation result shows the proposed method has the best performance, which could demonstrate the RNN has the ability in learning and predicting the time sequential CSI data in a changing environment. 1.3 Organizations The rest of this thesis is organized as follows. Chapter 2 briefly describes the basic concept, the architecture of the neural network and the mathematical algorithms used for training and their derivation. Chapter 3 considers a WiFi RSSI based indoor localization problem. After a full research of the existing approaches, we introduce a new two-step scheme using several DNNs, one of which is a classification network for clustering and the other are regression networks for final location prediction. In addition, a new RSSI fingerprinting pattern based on the RSSI similarity between closeby points is proposed and a me-

19 6 dian filter is applied as a pre-processor before the target RSSI is fed into the network. Real experiment result shows the improvement this two-step scheme could achieve. Chapter 4 extends our neural network study area to physical layer communication, a real-time CSI prediction system. Considering it could be formulated into a time sequential problem, we proposed a simple but efficient RNN, which is suitable for this type of problems, with an online training scheme based on the recent pilot assisted or data assisted CSI estimation. All the technical details are discussed and an initial simulation test is performed to demonstrate the ability of RNN in learning and analyzing the channel information. Chapter 5 concludes this thesis and enumerates open problems for further research.

20 7 Chapter 2 Neural Network 2.1 Perceptron The materials presented in this section follow [27]. In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector. Fig. 2.1 shows what a simple perceptron is like. A perceptron consists of Weight A perceptron can have multiple inputs (x[1], x[2],..., x[n] x[i] R), each of which has its corresponding weight w[i] R, with an additional weight call bias b, which is w[0] in the Fig Activation Function The step function is used. f(x) = { 1 x > 0 0 otherwise Output The output of this perceptron can be calculated as y = f(w T x + b) An Example of Perceptron Implementing Logic AND We design a simple perceptron to implement the logic AND function, to show the ability of the perceptron. Table 2.1 shows the truth table of the AND function.

21 8 Figure 2.1: A Simple Perceptron Table 2.1: Truth Table of the Logic AND x[1] x[2] y We can simply set w[1] = 0.5, w[2] = 0.5, b = 0.6, and choose the step function as the activation function. Thus this perceptron calculates the logic AND function. Check the line 1 in the truth table y = f(w T x + b) = f(w[1]x[1] + w[2]x[2] + b) = f( ) = f( 0.6) = 0 In fact, any linear classification problem can be solved by a perceptron. But if the data set is not linearly separable, the perceptron will never get to the state with all inputs classified into the correctly, for example, the logic XOR, which is a non-linear function.

22 9 2.2 Linear Unit and Gradient Descent The materials presented in this section follow [27] Linear Unit By replacing the step function with an identity function, a perceptron becomes a simple linear unit. Instead of just two values, 0 or 1, the output of a linear unit can be an arbitrary value, thus it can solve some non-linear regression problems. Fig. 2.2 shows the architecture of a simple linear unit with the activation function to be an identity function. f(x) = x Thus, the output of a linear unit can be calculated y = h(x) = f(w T x + b) = w T x + b = w[1] x[1] + w[2] x[2] + + w[n] x[n] + b where function h(x) is called hypothesis, whose parameters consist of w and b. By setting b = w[0] x[0] and x[0] = 1, the equation above can be writen as y = h(x) = f(w T x) = w T x Objective Function To train a linear unit, we need to minimize the error between the ground truth and the predicted value by the unit. There are a lot of functions to measure the error, among which, the mean square error is the most commonly used. e = 1 (y ȳ)2 2 where y is the actual value while ȳ is the predicted valued by the unit. By assuming n samples in the data set, the summation of the error of all the

23 10 Figure 2.2: A Simple Linear Unit samples is calculated as the error of the unit, E E = n i=1 = 1 2 = 1 2 = 1 2 e (i) n (y (i) ȳ (i) ) 2 i=1 n (y (i) h(x (i) )) 2 i=1 n (y (i) w T x (i) ) 2 i=1 where x (i), y (i), ȳ (i) and e (i) represent the input value, the actual output value, the predicted value and the error of the ith sample in the data set. Thus it can be seen that the purpose of training a linear unit is to minimize the error E by choosing a proper w, which is an optimization problem in mathematics and the E(w) is called the objective function. E(w) = 1 2 n (y (i) w T x (i) ) 2 i=1

24 Gradient Descent Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or approximate gradient) of the function at the current point. By calculating x new = x old η f(x) one can find the minimum of the function f(x), where η is called the learning rate. For the optimization problem mentioned in the previous subsection, the gradient descent algorithm can be written as w new = w old η E(w) By deriving the equation E(w), one can get E(w) = w E(w) = 1 n (y (i) ȳ (i) ) 2 w 2 i=1 = 1 n 2 w (y(i) ȳ (i) ) 2 i=1 = 1 n (y (i) ȳ (i) ) 2 ȳ (i) 2 ȳ (i) w i=1 = 1 n 2 = 1 2 = i=1 ȳ (i) ((y(i) ) 2 2y (i) ȳ (i) + (ȳ (i) ) 2 ) 2 n ( 2y (i) + 2ȳ (i) )x (i) i=1 n (y (i) ȳ (i) )x (i) i=1 w wt x (i) Thus the iteration step for this particular optimization problem is shown below w new = w old + η n (y (i) ȳ (i) )x (i) i=1

25 Neural Network and Backpropagation The materials presented in this section follow [27] Neuron Essentially, a neuron is the same as a perceptron, but with the activation function replaced by the sigmoid function. f(x) = sigmoid(x) = So the output of a neuron is calculated y = sigmoid(w T x) = e x e wt x The derivative of the sigmoid function is shown below f (x) = f(x)(1 f(x)) Thus, it is efficient to calculate the derivative of the sigmoid function as soon as one has calculated the value of the function Neural Network An NN is based on several collections of neurons which are connected with each other in a particular way. A neuron that takes the input from other neurons can process it and then send the result to the connected neurons for further use. Fig. 2.3 shows a simple fully connected neural network, from which one can figure out the characteristics of a fully connected neural network has The neurons are connected in layers. The left layer is called the input layer while the right is the output layer, and the layers between them are hidden layers as they are not seen from the outside. The neurons in the same layer do not have connections between each other. The neurons in one layer are connected to all the neurons in the previous layer.

26 13 Figure 2.3: A Simple Fully Connected Neural Network In fact, an NN is a function that maps the input vector x to the output vector y. To calculate the output of the NN, one needs to assign the input vector to the input layer, and then to calculate the value of each neuron in each layer in turn until all the values are calculated. The values of neurons in the output layer then form the output vector of the network. For example, the output of the fully connected NN in Fig. 2.3 is calculated as follows. The value of neuron 1, 2, 3 are the input value x[1], x[2], x[3]. To calculate the value of neuron 4, a 4 a 4 = sigmoid(w T x) = sigmoid(w 41 x[1] + w 42 x[2] + w 43 x[3] + w 4b ) where w 41, w 42 and w 43 are the weights of the connections between neuron 1, 2, 3 and neuron 4, and w 4b is the bias of neuron 4. By keeping doing this calculation, one can get the values of neuron 5, 6 and 7, followed by the value of neuron 8, 9 in the output

27 14 layer, y[1] = a 8 = sigmoid(w 84 a 4 + w 85 a 5 + w 86 a 6 + w 87 a 7 + w 8b ) y[2] = a 9 = sigmoid(w 94 a 4 + w 95 a 5 + w 96 a 6 + w 97 a 7 + w 9b ) [ ] y[1] Thus the output of the network y = is calculated based on the input vector y[2] x[1] x = x[2]. To be more clear, set x[3] Then, x[1] x = x[2] x[3], w 4 = 1 w 41 w 42 w 43 w 4b, w 5 = w 51 w 52 w 53, w 6 = w 61 w 62 w 63 w 5b w 6b w 7b, w 7 = w 71 w 72 w 73 By setting a = a 4 a 5 a 6 a 7, W = [ w 4 w 5 w 6 w 7 ] T = a 4 = sigmoid(w T 4 x) a 5 = sigmoid(w T 5 x) a 6 = sigmoid(w T 6 x) a 7 = sigmoid(w T 7 x) w 41 w 42 w 43 w 4b z 1 sigmoid(z 1 ) w 51 w 52 w 53 w 5b w 61 w 62 w 63 w 6b, sigmoid( z 2 ) = sigmoid(z 2 ).. w 71 w 72 w 73 w 7b Then, a = sigmoid(w x) where W, x and a is the weight matrix, the input vector and the output vector of

28 15 a certain layer. The above equation demonstrates that the effect of each layer of an NN is to apply a linear transformation to the input vector, followed by an activation function. The calculation process is the same for each layer, thus to calculate the output of the network, the above equation needs to be calculated repeatedly until the output layer Backpropagation To train an NN is to calculate the value of each weight w ij, but not the way how the neurons connect, the number of layers, the number of neurons in each layer, which are called hyper-parameters that are manually set. As mentioned in the previous section, the objective function needs to be formulated and then a gradient descent optimization algorithm can be applied to find the minimum. By using the mean square error to measure the error between the actual values and the predicted ones, the objective function of NN, E, and the gradient descent equation used are shown below, E = 1 2 i outputs (t i a i ) 2 w ji w ji η E w ji (2.1) where t i is the actual value of the ith neuron in the network. By analysis, one can find the weight w ji will only affect the rest of the network through the input to the neuron j, set s j to be the weighted summation of neuron j, s j = i w ji x ji = w T j x j where x ji is the value passed from neuron i to neuron j, x j is the input vector for neuron j. Thus E is a function of s j and s j is a function of w ji, by applying chain

29 16 rule one can get E = E w ji s j = E s j s j w ji = E s j x ji i w jix ji w ji By assigning δ j = E s j, the equation is also written as E w ji = δ j x ji For the neuron j in the output layer, E = E a j s j a j s j = ( 1 a j 2 i outputs (t i a i ) 2 ) sigmoid(s j ) s j = a j ( 1 2 (t j a j ) 2 )(a j (1 a j )) = (t j a j )a j (1 a j ) Thus δ j = (t j a j )a j (1 a j ). By plugging it into (2.1), the iteration step writes as w ji w ji η E w ji = w ji + η(t j a j )a j (1 a j )x ji = w ji + ηδ j x ji

30 17 For the neuron j in the hidden layer, E s j = = = = k Downstream(j) k Downstream(j) k Downstream(j) k Downstream(j) = (a j (1 a j )) E s k s k s j δ k s k s j δ k s k a j a j s j δ k w kj (a j (1 a j )) k Downstream(j) δ k w kj where Downstream(j) defines the neurons which are directly connected to the neuron j in the next layer. Thus δ j = (a j (1 a j )) k Downstream(j) δ kw kj. By plugging it into (2.1), the iteration step writes as w ji w ji η E w ji = w ji + η(a j (1 a j )) = w ji + ηδ j x ji k Downstream(j) δ k w kj x ji 2.4 Recurrent Neural Network and Backpropagation Through Time Recurrent Neural Network The materials presented in this subsection follow [6]. RNN is a type of NN that the neurons do not always feedforward, but connect to the neurons in the previous layer or the current layer itself. Thus RNN can use their internal state or memory to process the input so it is suitable for problems that can be formulated into a time sequence, such as natural language process and voice recognition. The left side of the Fig. 2.4, a simple RNN unit takes a time series of input data x and outputs o. The loop in the RNN unit makes it possible to pass the information

31 18 Figure 2.4: A Simple Recurrent Neural Network from one step to the next. In other words, an RNN unit can be treated as a horizontal expansion of the copies of itself. The right side of the Fig. 2.4 shows the network after the loop is unrolled, where x t, o t and s t denote the input, output and state at time step t. Thus the mathematical calculation of a general RNN is shown below o t = g(vs t ) (2.2) s t = f(ux t + Ws t 1 ) (2.3) where V, U and W are the weight matrix for output, input and state transformation, g and f are the activation functions for output and recurrent layer. (2.2) is the formula for the output layer of the network, which is a fully connected layer and (2.3) is the formula for the recurrent layer of the network, which calculates the s t based on x t and s t 1 with the additional weight matrix W Backpropagation Through Time The materials presented in this subsection follow [32]. Backpropagation Through Time (BPTT) is the algorithm that is used to update the weights in the recurrent layer of the recurrent neural network, the rationale of which is the same as Backpropagation described in the previous subsection. It consists of three steps, each of which is described in the following subsections. Calculate the value of each neuron forward. Calculate the error of each neuron backward.

32 19 Calculate the gradient for each weight. Forward for Value (2.3) is the formula to calculate the value of each neuron forward. Note that by assuming the input x is an m-dimension vector and the output o is an n-dimension vector, the dimensions of U and W are n m and n n. Unfold the equation to be more clear s t 1 u 11 u u 1m x t 1 w 11 w w 1n s t 2. = f( u 21 u u 2m x t w 21 w w 2n. 2. u n1 u n2... u nm w n1 w n2... w nn s t n x t m s t 1 1 s t 1 where the superscript and the subscript of x and s are the time step and the ordinal of the neuron. s t 1 n ) Backward for Error BTPP algorithm propagates the error δ l t in two directions, one into the previous layer δ l 1 t while the other back to the initial time step δ l 1. By setting net t = Ux t + Ws t 1, one can get s t 1 = f(net t 1 ). Thus net t net t 1 = net t = = s t 1 s t 1 net t 1 net t 1 net t s t 1 1 net... t 1 s t s t 1 n net t 2 net t s t 1 2 net... t 1 1 s t 1 2 s t 1 2 s t 1 2 n.... net t n net t s t 1 n net... t 1 s t 1 n 2 s t 1 n w 11 w w 1n f (net t 1 w 21 w w 2n.. w n1 w n2... w nn = Wdiag[f (net t 1 )] s t 1 1 net t 1 net t 1 1 s t 1 n net t 1 1 s t 1 1 net t 1 1 s t 1 2 net t 1 1. s t 1 n net t s t 1 1 net t 1 n s t 1 2 net t 1 n. s t 1 n net t 1 n 1 ) f (net t 1 2 ) f (net t 1 n ).

33 20 Then the equation for the propagation into the initial time step is δ T k = E net k = E net t net t net k = E net t... net k+1 net t net t 1 net k t 1 = δ T t Wdiag[f (net i )] i=k By setting at l 1 as the output of the previous layer, one can get net l t = Ua l 1 t + Ws t 1. Thus the equation for the propagation into the previous layer is (δ l 1 t ) T = E net l 1 t = E net l t = E net l t net l t net l 1 t net l t a l 1 t a l 1 t net l 1 t = (δ l t) T U[f l 1 (net l 1 t )] where f l 1 is the activation function of the previous layer. Gradient The calculation of gradient for W and U is separated, but similar. E w ji = = = t k=1 t k=1 t k=1 E k w ji E k net k j δ k j s k 1 i net k j w ji

34 21 = E u ji = k=1 t k=1 E k u ji t E k net k j net k j u ji t = δj k a k i k= Gradient Vanishing and Explosion The materials presented in this subsection follow [32]. Unfortunately, RNN cannot achieve good performance for long sequences. One main reason is gradient vanishing and explosion in training, which leads to the fact that the gradient cannot propagate long enough. Check the formula below δ T k = δ T t t 1 Wdiag[f (net i )] i=k t 1 δ T k δ T t W diag[f (net i )] i=k δ T t (β W β f ) t k where β defines the upper bound of the modulus of the matrix. Thus if t k is big enough, the error δk t will increase or decrease very quickly, depending on the value of β bigger or smaller than 1, which causes the vanishing and explosion problem. 2.5 Long Short Term Memory Networks The materials presented in this section follow [30, 26]. To solve the gradient vanishing and explosion problem in general RNN, long short term memory (LSTM) networks, a special kind of RNN which are capable of learning long-term dependencies, will be introduced in the section. LSTMs are explicitly designed to avoid the long-term dependency problem and remembering information for long periods of time is practically their default behaviour. The key to LSTMs is the cell state, c t in the Fig. 2.5, to which the LSTM does have the ability to remove or add information, carefully regulated by structures called gates. Gates are a way to optionally let information through. They are composed

35 22 Figure 2.5: The Structure of a LSTM Cell out of a sigmoid neural net layer and a pointwise multiplication operation. An LSTM has three of these gates, a forget gate, an input gate and an output gate, to protect and control the cell state Forward for Value The first step in LSTM is to decide what information is going to be thrown away from the cell state. This decision is made by a sigmoid layer called the forget gate layer. It looks at h t 1 and x t and outputs a number between 0 and 1 for each number in the cell state c t1. where f t = σ(w f [h t 1, x t ] ) [ ] a, b means to concatenate two vectors into one vector. The next step is to decide what new information is going to be stored in the cell state. This has two parts, a sigmoid layer called the input gate layer decides which

36 23 values well update and a tanh layer creates a vector of new candidate values, c t, that could be added to the state. In the next step, these two are combined to create an update to the state. where means the pointwise multiplication. ] i t = σ(w i [h t 1, x t ) (2.4) ] c t = tanh(w c [h t 1, x t ) (2.5) c t = f t c t 1 + i t c t (2.6) Finally, the output will be based on the cell state but will be a filtered version. A sigmoid layer which decides what parts of the cell state are going to be output is run first and then we put the cell state through tanh and multiply it by the output of the sigmoid gate so that we only output the parts we decided to. o t = σ(w o [h t 1, x t ] ) (2.7) h t = o t tanh(c t ) (2.8) Backward for Error From (2.6), one can get From (2.8), one can get c t f t = diag(c t 1 ) c t i t = diag( c t ) c t c t = diag(i t ) h t o t = diag[tanh(c t )] h t c t = diag[o t (1 tanh(c t ) 2 )]

37 24 Also, the following variables are defined Thus, net f,t = W f [ h t 1, x t ] = W fh h t 1 + W fx x t net i,t = W i [ h t 1, x t ] = W ih h t 1 + W ix x t net c,t = W c [ h t 1, x t ] = W ch h t 1 + W cx x t net o,t = W o [ h t 1, x t ] = W oh h t 1 + W ox x t δ f,t = E net f,t δ i,t = E net i,t E δ c,t = δ o,t = net c,t E net o,t f t net f,t = diag[f t (1 f t )] net f,t h t 1 = W fh i t net i,t = diag[i t (1 i t )] net i,t h t 1 = W ih c t net c,t = diag[1 c 2 t ] net c,t h t 1 = W ch o t net o,t = diag[o t (1 o t )] net o,t h t 1 = W oh

38 25 Then the equation for the propagation into the previous time step is δ T t 1 = E h t 1 = E h t h t = δ T h t t = δ T t +δ T t h t 1 h t 1 h t c t c t f t h t c t c t c t f t net f,t net f,t h t 1 c t net c,t + δ T t net c,t h t 1 + δ T h t c t i t net i,t t c t i t net i,t h t 1 h t o t net o,t o t net o,t h t 1 = δ T t [o t (1 tanh(c t ) 2 )] [c t 1 ] [f t (1 f t )]W fh +δ T t [o t (1 tanh(c t ) 2 )] [ c t ] [i t (1 i t )]W ih +δ T t [o t (1 tanh(c t ) 2 )] [i t ] [(1 c t ) 2 ]W ch +δ T t [tanh(c t )] [o t (1 o t )]W oh = δ T f,tw fh + δ T i,tw ih + δ T c,tw ch + δ T o,tw oh By defining the error of the previous layer δ l 1 t = E and the input of the net l 1 t current LSTM layer x l t = f l 1 (net l 1 t ), where f l 1 is the activation function of the previous layer. Thus the equation for the propagation into the previous layer is E net l 1 t = E net l f,t net l f,t x l t + E net l c,t net l c,t x l t = δ T f,tw fx f l 1 (net l 1 t x l t + E net l i,t net l 1 t net l i,t x l t x l t + E net l 1 t net l o,t net l o,t x l t x l t net l 1 t x l t net l 1 t ) + δ T i,tw ix f l 1 (net l 1 t ) +δ T c,tw cx f l 1 (net l 1 t ) + δ T o,tw ox f l 1 (net l 1 t )

39 Gradient The calculation of gradient for W fh, W ih, W ch, W oh, W fx, W ix, W cx and W ox is separated, but similar. E W fh = = = E W ih = E W ch = E W oh = E W fx = t E j W j=1 fh t j=1 E j net f,j net f,j W fh t δ f,j h T j 1 j=1 t δ i,j h T j 1 j=1 t j=1 δ c,j h T j 1 t δ o,j h T j 1 j=1 E net f,t net f,t W fx = δ f,t x T t E W ix = δ i,t x T t E W cx = δ c,t x T t E W ox = δ o,t x T t

40 27 Chapter 3 Deep Neural Network in Indoor Positioning System with a Two-Step Scheme 3.1 Introduction The LBSs have been driven so fast by the rapid proliferation of wireless communication and mobile devices, which raises a massive demand for high accuracy of localization. For the outdoor open environment, customers can use the GNSS, such as Global Positioning System (GPS) and BeiDou Navigation System, to obtain a highly accurate location estimation. However, the GNSS signals from satellites cannot be seen in many indoor areas, which limits their applications in indoor localization. Therefore, people turn to different sensor-based systems, such as Bluetooth [1, 35], RFID [20] and ultrasound [33], to solve the localization problem in the indoor environment. Among all these available solutions, WiFi-based IPS becomes one of the promising approaches because of the popularity of wireless local area network (WLAN) infrastructure and the fast development of mobile devices, which makes the system low cost and easy to deploy. In general, WiFi IPSs can be classified into two dominant classes, ranging based and fingerprinting based. Ranging based ones derive the distances between the receiver and different transmitters based on propagation models, using measurements such as time of flight, received signal strength and angle of arrival [22], and then estimate the location based on the distances obtained in the first step by triangula-

41 28 tion. However, due to the multi-path phenomenon, the accurate propagation model is difficult to formulate, leading to the inaccuracy of the distance prediction. The fingerprinting based methods, which associate a group of physical measurements at each RP as a fingerprint, perform like pattern matching systems, comparing the similarity between the target fingerprint and those in the database to return the best match to be the estimation. Thus a fingerprinting system consists of two phases, an offline phase, collecting fingerprints at different RPs within the surveillance area and storing them into a database, and an online phase, comparing the target fingerprint with those in the database to return the best match as the prediction based on the desired pattern matching algorithm. Received signal strength indicator (RSSI)-based WiFi fingerprinting IPSs have been intensively studied in the past decade as the RSSI value is available in every interface. There are some other approaches using different physical measurements such as CSI [38, 7] as the fingerprints, but they need special WiFi devices and increase the deployment and system cost. When it comes to the online phase, the IPS needs to calculate the location of the unknown node, which is usually adopted by experts systems, such as KNN [4, 29, 39, 42], SVM [34, 21], filter-based [5, 3] and NN based algorithms. KNN calculates the distance between the target fingerprint and those in the database to get a set of nearest neighbours and return the mean as the final prediction. To calculate the distance, researchers use different metrics, such as Euclidean distance [4], Bhattacharyya distance [29], Spearman distance [39] and so on. Zou et al. proposed a weighted KNN to improve the accuracy by returning a weighted average instead of the mean [42]. SVM, a machine learning algorithm which is simpler than a multi-layer neural network, builds a model that maps the fingerprints into a high dimensional space and then find a hyperplane that differentiates the classes based on all the training points. Principal component analysis (PCA) and Kernel SVM [21] are used to reduce the high dimensional measurements. Recently, some filter based algorithms are designed to improve the accuracy by taking the previous prediction into account. For example, Kalman filter [5, 3] is used to calculate the most likely location assuming a Gaussian noise and linear motion dynamics. In contrast, NN based algorithms build up a neural network that predicts the location from the target input by defining a particular architecture using different activation functions. In this chapter, we propose a new NN-based IPS that contains multiple NNs including one classification network and several localization networks, to reduce the training complexity and improve the predicting accuracy. The proposed system uti-

42 29 lizes the similarity in RSSI readings within a specific region to distribute the target fingerprint into a cluster that it belongs to by the classification network and then applies the corresponding localization network to evaluate a final prediction. There are different approaches to reduce the workload of building up the initial database for offline training, but our RSSI fingerprint database is collected in our lab by a selfdeveloped 3-wheel robot, which is shown in Fig It has multiple sensors including wheel odometer, an inertial measurement unit (IMU), a LIDAR, sonar sensors and a colour and depth (RGB-D) camera. The robot can navigate to a target location to collect WiFi fingerprints automatically. Therefore, the time consumption for building up the fingerprint database is significantly reduced. The rest of the chapter is organized as follows. Section 3.2 introduces the related work on NN in IPS, followed by the detail model in Section 3.3. Section 3.4 compares the result with other approaches, and the conclusion of the proposed work is given in Section 3.5 for this chapter. 3.2 Related Work Fingerprinting Technique The fingerprinting-based IPS works like a pattern matching system, whose primary design can be divided into two parts, an offline and an online phase. In the offline stage, fingerprints at different RPs within the surveillance area need to be collected and stored in a database for the next step, which is also called a site survey. During the online stage, by comparing a target fingerprint at an unknown location with those in the database based on a well-designed algorithm, the system then returns the best match as the current prediction. While most of the fingerprinting systems are relying on WiFi RSSI, some use Bluetooth [1, 35], RFID [20], and ultrasound [33] devices RSSI and some others use CSI [38, 7] as the fingerprint. Although these systems provide suitable accuracy, they often focus on objective tracking and need corresponding hardware other than the WiFi devices.

43 30 Figure 3.1: The three-wheel robot developed by my colleagues NN based IPSs Depending on the output type of the network, existing NN based IPSs can be grouped into two categories, classification and regression. The classification type outputs the predicted label of the unknown location while the regression type directly returns the exact coordinates. In the literature, multilayer perceptron (MLP) or feed forward neural network is the most frequently used NN for IPS. Fang et al. presented a discriminant-adaptive neural network (DANN), which is implemented by a 3-layer MLP plus multiple dis-

44 31 criminant analysis (MDA), outputting the predicted coordinate directly [14]. A real experiment result showed that DANN is more accurate than KNN, maximum likelihood (ML) and simple MLP, with a mean error of smaller than 2 m. In [19], Dai et al. employed an MLP based IPS classifier with a boosting training method, which achieved higher accuracy compared with ML and generalized regression neural network (GRNN) in the experiments. By using the CSI as fingerprints, Chen et al. developed ConFi, the first system based on CNN, which takes the CSI as input images and is trained to solve a location classification problem and has a mean localization error of 1.36 m and the standard deviation is 0.90 m for the configured experiment [7]. Lukito [24] et al. implemented an RNN model which has two layers of Elman Simple RNN and takes the RSSI readings directly as input and outputs the location labels using Tensorflow. The classification accuracy of this system is 82.47% which is better compared to multi-layer perceptron, Nave Bayes, J48, and SVM, but the network still needs to be tweaked to surpass KNN Clustering based IPSs To reduce the computational complexity and improve the positioning time as well as the positioning accuracy, many researchers came up with the idea of clustering. By utilizing nearest neighbor rule and extreme learning machine (ELM), Xiao et al. proposed a novel clustering base IPS for large scale area [37]. The system applies clustering based on nearest neighbor rules and localization by ELM, giving an approximately 1 m better mean accuracy than that without clustering with the same time complexity. In 2015, Chen et al. proposed a clustering approach: AP similarity clustering and K-weighted nearest node (KWNN) method, which divides the database into clusters based on different APs similarity [9]. In the online test phase, the system finds out the suitable sub-cluster first and then selects k nodes among the cluster and return the k-weighted prediction, improving the accuracy by 17.14% and reducing the time-consuming by 50% with an average error of 0.77 m compared to k-means+kwnn and KWNN-only.

45 32 (a) (b) Figure 3.2: (a) Floor map of surveillance area which could be divided into 5 clusters. (b) Heat map of the RSSI strength from 6 APs used in our localization scheme.